Perform peg-in-hole task with unknown tilt

ABSTRACT

A computer-implemented method executed by a robotic system for performing a positional search process in an assembly task is presented. The method includes applying forces to a first component to be inserted into a second component, detecting the forces applied to the first component by employing a plurality of force sensors attached to a robotic arm of the robotic system, extracting training samples corresponding to the forces applied to the first component, normalizing time-series data for each of the training samples by applying a variable transformation about a right tilt direction, creating a time-series prediction model of transformed training data, applying the variable transformation with different directions for a test sample, and calculating a matching ratio between the created time-series prediction model and the transformed test sample.

BACKGROUND Technical Field

The present invention relates generally to robotic assembly, and morespecifically, to performing a peg-in-hole task with unknown tilt.

Description of the Related Art

Over the years, shifting manufacturing requirements to high flexibility,short production cycle time, and high throughput have enabled theemergence of intelligent manufacturing systems. Conventional industrialrobots have high repeatability, but may lack adaptivity and flexibility.In manufacturing processes, the environment is constantly changing andparts and/or components to be processed could come from differentbatches and different suppliers. All of these variations can causedifficulty for conventional industrial robots to perform variousmanufacturing processes. Due to demanding requirements of manufacturingand limitations of conventional industrial robots, intensive humanlabors have been made in robot programming.

SUMMARY

In accordance with one embodiment, a computer-implemented methodexecuted by a robotic system for performing a positional search processin an assembly task is provided. The computer-implemented methodincludes applying forces to a first component to be inserted into asecond component, detecting the forces applied to the first component byemploying a plurality of force sensors attached to a robotic arm of therobotic system, extracting training samples corresponding to the forcesapplied to the first component, normalizing time-series data for each ofthe training samples by applying a variable transformation about a righttilt direction, creating a time-series prediction model of transformedtraining data, applying the variable transformation with differentdirections for a test sample, and calculating a matching ratio betweenthe created time-series prediction model and the transformed testsample.

In accordance with another embodiment, a robotic system for performing apositional search process in an assembly task is provided. The roboticsystem includes a robotic arm and a control system communicativelycoupled to the robotic arm, the control system storing executableprogram instructions for causing the robotic arm to perform the steps ofapplying forces to a first component to be inserted into a secondcomponent, detecting the forces applied to the first component byemploying a plurality of force sensors attached to the robotic arm,extracting training samples corresponding to the forces applied to thefirst component, normalizing time-series data for each of the trainingsamples by applying a variable transformation about a right tiltdirection, creating a time-series prediction model of transformedtraining data, applying the variable transformation with differentdirections for a test sample, and calculating a matching ratio betweenthe created time-series prediction model and the transformed testsample.

In accordance with yet another embodiment, a robotic system is provided.The robotic system includes a robot constructed to assemble a firstcomponent to a second component, at least one sensor coupled to therobot, a control system communicatively coupled to the robot and to theat least one sensor, the control system storing executable programinstructions for executing assembly motion of the robot, and a learningdevice communicatively coupled to the control system and operative todirect the robot via the control system. The control system performs thesteps of extracting training samples corresponding to the forces appliedto the first component, normalizing time-series data for each of thetraining samples by applying a variable transformation about a righttilt direction, creating a time-series prediction model of transformedtraining data, applying the variable transformation with differentdirections for a test sample, and calculating a matching ratio betweenthe created time-series prediction model and the transformed testsample.

Furthermore, embodiments can take the form of a related computer programproduct, accessible from a computer-usable or computer-readable mediumproviding program code for use, by or in connection with a computer orany instruction execution system. For the purpose of this description, acomputer-usable or computer-readable medium can be any apparatus thatmay include means for storing, communicating, propagating ortransporting the program for use, by or in a connection with theinstruction execution system, apparatus, or device.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The invention will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block/flow diagram of an exemplary robotic system, inaccordance with an embodiment of the present invention;

FIG. 2 is a block/flow diagram of an exemplary robotic system in a workcell, in accordance with an embodiment of the present invention;

FIG. 3 is a block/flow diagram of an exemplary peg-in-hole assemblyemployed in describing the robotic system, in accordance with anembodiment of the present invention;

FIG. 4 is a cross-sectional view of a first component being successfullyinserted into a second component via a robotic arm of the roboticsystem, in accordance with an embodiment of the present invention;

FIG. 5 is a block/flow diagram of an exemplary training phase and testphase, in accordance with an embodiment of the present invention;

FIG. 6 is a block/flow diagram of exemplary estimation results of tiltdirection, in accordance with an embodiment of the present invention;

FIG. 7 is a block/flow diagram of an exemplary method for performing apositional search process in an assembly task, in accordance with anembodiment of the present invention; and

FIG. 8 is a block/flow diagram of an exemplary method for manipulatingtraining samples and test samples to accomplish the peg-in-hole task, inaccordance with an embodiment of the present invention.

Throughout the drawings, same or similar reference numerals representthe same or similar elements.

DETAILED DESCRIPTION

Embodiments in accordance with the present invention provide methods anddevices for employing a robotic system. The robotic system is controlledto employ assembly processes. One assembly process includes assembling afirst component to a second component. The assembly process can broadlyinclude two main phases. The first phase is a search phase and thesecond phase is an insertion phase. In the search phase, the firstcomponent is brought within a clearance region. In the insertion phase,an assembly of the first component and the second component takes place.Robotic systems are dynamic systems. Most of the dynamic systems arecomplex, nonlinear, and time varying. A variety of control techniquescan be employed for dynamic systems. One such technique involvesemploying training samples to be compared to test samples to accomplisha peg-in-hole task.

Embodiments in accordance with the present invention provide methods anddevices for implementing robotic systems with best operating conditionsbased on learning or training techniques. The robotic system canlearn-by-doing by employing feedback from learning or training that isstored in memory and made available in accordance with presentconditions. For example, if two parts are to be assembled, the two partsare identified along with their best conditions to identify a bestassembly strategy.

It is to be understood that the present invention will be described interms of a given illustrative architecture; however, otherarchitectures, structures, substrate materials and process features andsteps/blocks can be varied within the scope of the present invention. Itshould be noted that certain features cannot be shown in all figures forthe sake of clarity. This is not intended to be interpreted as alimitation of any particular embodiment, or illustration, or scope ofthe claims.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIG. 1, a block/flow diagram of anexemplary robotic system is presented, in accordance with an embodimentof the present invention.

The block diagram 10 depicts a robotic system 12 in communication with acontrol system 14. The robotic system 12 can include one or more robots.The control system 14 is in communication with a training/learningsystem 15 and sensors 16. The control system 14 further communicateswith input devices 18 and displays 19.

In one exemplary embodiment, control system 14 includes a dedicatedrobot controller and a data processing unit or controller 2. The robotcontroller and the input devices 18 can be communicatively coupled tothe data processing controller. In one exemplary embodiment, the robotcontroller operates the robotic system 12 based on data provided by thedata processing controller, which receives control input from anothersystem or device, e.g., input devices 18 and training/learning system15. The training/learning system 15 can adjust operating conditions ofthe robotic system 12 in order for the robotic system to perform at anoptimal level based on best operating conditions derived from learningtechniques.

Control system 14 can be microprocessor-based and the programinstructions executed thereby are in the form of software stored in amemory 4. However, it is alternatively contemplated that any or all ofthe controllers and program instructions can be in the form of anycombination of software, firmware and hardware, including statemachines, and can reflect the output of discreet devices and/orintegrated circuits, which can be co-located at a particular location ordistributed across more than one location, including any digital and/oranalog devices configured to achieve the same or similar results as aprocessor-based controller executing software and/or firmware and/orhardware based instructions.

In some embodiments, robotic system 12 can include one or more sensors16, e.g., for use in operating robotic system 12 locally or remotely,for enhancing safety, and/or for other purposes. Sensors 16 can take anysuitable form, e.g., including vision sensors such as cameras, acousticsensors, infrared sensors or one or more other types of proximitysensors, microphones, position sensors, translational and rotationalspeed sensors, force sensors and/or any other types of sensors. Sensors16 are communicatively coupled to control system 14. In someembodiments, control system 14 can include a controller communicativelycoupled to one or more sensors 16 for processing the output of one ormore sensors 16.

In one exemplary embodiment, input device 18 is a joystick. In otherembodiments, input device 18 can take other forms, e.g., a stylus. Inputdevice 18 can be constructed to allow the user to control or initiatethe motions or movements of robotic system 12, e.g., via control system14. In some embodiments, input device 18 can be constructed to controlor initiate a position, direction and/or speed of rotational andtranslational motion of robotic system 12, e.g., end effector 28 (FIG.2) based on feedback received from the training/learning system 15 inorder to achieve best operating conditions for the robotic system 12.

In some embodiments, robotic system 12 includes one or more displaydevices 19 communicatively coupled to the data processing controller ofcontrol system 14. In one exemplary embodiment, display devices 19 arealso input devices, e.g., a touch screen display. Display devices 19display, for example, robot motion data, and can be employed to adjustor fine-tune parameters or variables to obtain best operating conditionsbased on the training/learning system 15.

The training/learning system 15 learns how to better understand thephysical interaction model and to perform the assembly task. Thephysical interaction model relates to, e.g., exchanged forces and/ormoments between the robotic system 12 and the environment. Thus, thememory based system is trained by using reinforcement learning.Reinforcement learning is conducted by choosing or selecting an actionamong decomposed actions and assembly movement actions at each step ofthe positional search process based on, e.g., corresponding force-torquedata received from at least one sensor 16 associated with the roboticsystem 12.

Reinforcement learning problem setting can be considered as follows:

The robotic system 12 observes the environmental state to decide anaction the robotic system 12 wishes to take. The environment can changeaccording to a certain rule and a human can change the environment byhis or her own action. A reward signal is returned every time an actionis taken. The sum of the rewards in the future is to be maximized.Learning starts in a state in which a result to be brought about by theaction is totally unknown or known only incompletely. In other words,the robotic system 12 can obtain the result of an action as data onlyafter the robotic system 12 actually takes the action. This means thatan optimal action can be searched for by, e.g., trial and error.Learning can be started from a good starting point by starting from aninitial state in which learning has been performed in advance. Inreinforcement learning, in addition to determination and classification,an action is learned to acquire a method for learning an appropriateaction in consideration of interactions exerted on the environment bythe action, e.g., learning to maximize the reward to be obtained in thefuture.

In one example, the reinforcement learning can be employed by thetraining/learning system 15 and can be implemented by, e.g., deepmachine learning methods. The exemplary embodiments of the presentinvention can be directed generally to deep machine learning methods andapparatuses related to manipulation of an object by an end effector of arobot. Some implementations are directed to training a deep neuralnetwork, such as a convolutional neural network (also referred to hereinas a “CNN”), to predict a probability that motion data for an endeffector of a robot results in successful assembly of a first componentto a second component by the end effector. For example, someimplementations enable applying, as input to a trained deep neuralnetwork, at least: (1) a motion vector that defines a candidate motionof an insertion end effector of a robot and (2) an image that capturesat least a portion of the work space of the robot; and generating, basedon the applying, at least a measure that directly or indirectlyindicates a probability that the motion vector results in successfulinsertion of the first component to the second component. The predictedprobability can then be used in determining best operating conditionsand monitoring performance of insertion attempts by the robotic systemhaving an insertion end effector, thereby improving the ability of therobotic system to successfully insert the first component into thesecond component.

Some implementations of the training/learning system 15 can be directedto, e.g., utilization of the trained deep neural network to servo an endeffector of a robot to achieve successful insertion of the firstcomponent into the second component. For example, the trained deepneural network can be utilized in the iterative updating of motioncontrol commands for one or more actuators of a robot that control aposition of an insertion end effector of the robot, and to determinewhen to generate insertion control commands to effectuate an attemptedinsert by the insertion end effector. In various implementations,utilization of the trained deep neural network to servo the insertionend effector can enable fast feedback to robotic perturbations and/ormotion of environmental object(s) and/or robustness to inaccuraterobotic actuation(s). The trained deep neural network can also enablereduction in the number of perturbations in order to achieve bestoperating conditions of the robotic system 12.

In some implementations of the training/learning system 15, a method canbe provided that, e.g., includes generating a candidate end effectormotion vector that defines motion to move an insertion end effector of arobot from a current position to a subsequent position that enables moreefficient assembly strategies. The method can, in one example, furtherinclude identifying a current image that is captured by a vision sensorassociated with the robotic system 12 and that captures the insertionend effector and at least one object in an environment of the roboticsystem 12. The method can further include applying the current image andthe candidate end effector motion vector as input to a trainedconvolutional neural network and generating, over the trainedconvolutional neural network, a measure of successful inserts of theobject with application of the motion. The measure is generated based onthe application of the image and the end effector motion vector to thetrained convolutional neural network.

In some implementations of the training/learning system 15, a method canbe provided that includes, e.g., identifying a plurality of trainingexamples generated based on sensor output from one or more robots duringa plurality of insert attempts by the robots. Each of the trainingexamples including training example input and training example output.The training example input of each of the training examples includes: animage for a corresponding instance of time of a corresponding insertattempt of the insert attempts, the image capturing a robotic endeffector and one or more environmental objects at the correspondinginstance of time, and an end effector motion vector defining motion ofthe end effector to move from an instance of time position of the endeffector at the corresponding instance of time to a final position ofthe end effector for the corresponding insert attempt. The trainingexample output of each of the training examples can include, e.g., aninsert success label indicative of success of the corresponding insertattempt. The method further includes training the convolutional neuralnetwork based on the training examples to achieve best operatingconditions for the robotic system 12.

In some implementations of the training/learning system 15, training theconvolutional neural network includes applying, to the convolutionalneural network, the training example input of a given training exampleof the training examples. In some of those implementations, applying thetraining example input of the given training example includes: applyingthe image of the given training example as input to an initial layer ofthe convolutional neural network and applying the end effector motionvector of the given training example to an additional layer of theconvolutional neural network. The additional layer can be downstream ofthe initial layer. In some of those implementations, applying the endeffector motion vector to the additional layer includes: passing the endeffector motion vector through a fully connected layer to generate endeffector motion vector output and concatenating the end effector motionvector output with upstream output. The upstream output can be from animmediately upstream layer of the convolutional neural network that isimmediately upstream of the additional layer and that is downstream fromthe initial layer and from one or more intermediary layers of theconvolutional neural network. The initial layer can be a convolutionallayer and the immediately upstream layer can be a pooling layer.

In some implementations, the training includes performingbackpropagation on the convolutional neural network based on thetraining example output of the plurality of training examples.Therefore, the learning/training system 15 can have the function ofextracting, e.g., a useful rule, a knowledge representation, and adetermination criterion by analysis from a set of data input to thelearning/training system 15, outputting determination results, andlearning knowledge (machine learning). It is noted that a variety ofmachine learning techniques are available, which can be roughlyclassified into, e.g., “supervised learning,” “unsupervised learning,”and “reinforcement learning.” To implement these techniques, “deeplearning” can be employed, as discussed above.

FIG. 2 is a block/flow diagram of an exemplary robotic system in a workcell, in accordance with an embodiment of the present invention.

In one exemplary embodiment, the robotic system 12 can be a multi-axisindustrial robot disposed in, e.g., a work cell 20. The assembly workcan be automated and triggered to be initiated by a user. For example,robotic system 12 can be initiated or triggered by using input devices18 from any location outside of work cell 20 to assemble a firstcomponent, generically represented as component 25, to a secondcomponent, generically represented as component 32, e.g., disposed on awork table or fixture 30. For instance, robotic system 12 can beoperated to insert component 25 into an opening 34 of component 32. Therobotic system 12 can use learned techniques in order to be optimallyprogrammed based on best operating conditions. For example, the roboticsystem 12 employs feedback from learning/training that is stored in thememory 4 and made available in accordance with the present conditions tocontinuously adjust or fine-tune operations to an optimal level. Invarious embodiments, robotic system 12 can take any form suited to theapplication for which it is employed, and can be any type of robotconstructed to perform any type of manufacturing work or otheroperation.

In one exemplary embodiment, robotic system 12 can include a pedestal26, a shoulder 24 coupled to and rotatable about pedestal 26, and anupper arm or rotatable arm 22 coupled to shoulder 24. The rotatable arm22 culminates in a rotatable end effector 28. In other exemplaryembodiments, robotic system 12 can have a greater or lesser number ofappendages and/or degrees of freedom. In one exemplary embodiment, endeffector 28 is configured to grip and manipulate component 25 forassembly with component 32 based on input received from thetraining/learning system 15. In other exemplary embodiments, endeffector 28 can take other forms, and can be configured for performingother operations, e.g., any operations related to or unrelated tocomponent 25. Robotic system 12 can be constructed to translate androtate component 25 in a minimal number of steps, in and about the X, Y,and Z axes, e.g., as illustrated in FIG. 3.

In some exemplary embodiments, robotic system 12 can have associatedtherewith a haptic feedback sensor 27. The sensor 27 can be operative todetect interactions between component 25 and anything else in itsimmediate environment, e.g., physical interactions between component 25(e.g., while held by robotic system 12) and component 32, or betweencomponent 25 and anything within the reach of robotic system 12. In oneexemplary embodiment, haptic feedback sensor 27 is a force sensor. Inother embodiments, haptic feedback sensor 27 can take other forms. Forcesensor 27 can be communicatively coupled to control system 14. In oneexemplary embodiment, sensor 27 can be mounted on robotic system 12,e.g., on end effector 28. In other embodiments, sensor 27 can be mountedat any suitable location or on any suitable feature of robotic system 12or component 25.

FIG. 3 is a block/flow diagram of an exemplary peg-in-hole assemblyemployed in describing the robotic system, in accordance with anembodiment of the present invention.

Some aspects of a non-limiting example of a peg-in-hole assembly areemployed in describing a non-limiting example of an embodiment of thepresent invention. In FIG. 3, a first component, peg 25, is sought to beinserted into a hole 34 in a block 32. In difficult assembly cases,e.g., where the clearance between peg 25 and hole 34 is low and anychamfers on peg 25 and hole 34 are small, manual insertion usingtele-operated motion alone can be difficult, even with haptic feedback.For example, a slight misalignment between the components might resultin jamming or binding.

FIG. 4 is a cross-sectional view of a first component being successfullyinserted into a second component via a robotic arm of the roboticsystem, in accordance with an embodiment of the present invention.

The first component 25 is shown to be successfully received within thehole 34 of the second component 32. The first component 25 is configuredto be flush with the inner walls of the second component 32. This isachieved by the training/learning system 15. Some implementations of thetraining/learning system 15 can be directed to training a deep neuralnetwork, such as a CNN, to enable utilization of the trained deep neuralnetwork to predict a measure indicating the probability that motion datafor an insertion end effector of a robot results in a successfulinsertion of the first component 25 into the second component 32. Insome implementations, the trained deep neural network accepts an imagegenerated by a vision sensor and accepts an end effector motion vector.The application of the image and the end effector motion vector to thetrained deep neural network can be used to generate, over the deepneural network, a predicted measure that executing command(s) toimplement the motion defined by motion vector, and subsequent inserting,will produce a successful insertion of the first component 25 into thesecond component 32. Some implementations are directed to utilization ofthe trained deep neural network to servo the end effector of a robot toachieve successful insertion of the first component 25 into the secondcomponent 32 in a minimal number of steps based on the feedback receivedfrom the training/learning system 15.

FIG. 5 is a block/flow diagram of an exemplary training phase and testphase, in accordance with an embodiment of the present invention.

The following assumptions are made for the data properties:

Data is a time-series of data that can be obtained by applying random xyforces for a certain time period. The forces can be measures by aplurality of force sensors.

One training sample can include six dimensional time-series data, andright tilt direction(θ) can be obtained as follows:

Data: inFx, inFy: input forces on xy direction.

Data: Fx, Fy: force sensor values on xy directions.

Data: Mx, My: force sensor moments around xy axes.

If the tilt magnitude needs to be estimated, a right tilt magnitude (φ)can also be added.

In the training phase:

For each training sample, the method normalizes time-series data byapplying a variable transformation about the right tilt direction (θ) asfollows:

inFx′=inFx cos(−θ)−inFx sin(−θ)

inFy′=inFx sin(−θ)+inFx cos(−θ)

The same variable transformation is applied for (Fx, Fy) and (Mx, My)pairs.

A time-series model of transformed training data can now be built orcreated.

For a time-series prediction model, Vector Auto Regression (VAR) can beused.

The transformed time-series data should have the same or similarcharacteristics as a time-series data.

In the test phase:

For a test sample, the variable transformation is applied with differentdirections. (e.g., 10 deg, 20 deg, 30 deg, etc.)

The matching ratio between the model created in the training phase andeach of transformed test data is then calculated.

For the matching ratio, the sum of squares of each time point and eachdimension can be employed.

As a result, the direction value that has best matching value can beoutput as an estimation result (estimation for tilt direction).

In the training phase 40, a set of samples 42, 44, 46, 48 can beprocessed to create a time series prediction model of transformedtraining data 50. Such transformed training data 50 is compared to atleast one test sample. Thus, in a testing phase 60, a test sample isselected and variable transformation with different directions isapplied to the selected test sample to output estimation results 62, 64,66, 68. The estimation results are provided for different tiltdirections (e.g., 10 degrees, 30 degrees, 350 degrees).

Therefore, the exemplary embodiments pertain to a control algorithm fora robot. The control algorithm controls the insertion of a peg in ahole. The peg-in-hole task employs time-series force sensor information.The control algorithm processes time-series data by applying variabletransformation with different directions on testing samples andcalculates a matching ratio between a prediction model built in thetraining phase and each of the transformed test data. In other words, ina training phase, training data is acquired and a time-series predictionmodel is created. Then in a test phase, a test sample is selected andvariable transformation with different directions is applied to theselected test sample. A matching ratio can now be calculated between thetime-series prediction model and the transformed data sample to obtainan estimation result (estimation of tilt direction).

FIG. 6 is a block/flow diagram of exemplary estimation results of tiltdirection, in accordance with an embodiment of the present invention.

Diagram 70 is a side view and diagram 72 is a top view of an object 25attempting to be inserted, by, e.g., a robotic arm of a robotic system,within an opening 34 defined by component 32. Diagram 70 illustrates thetilt magnitude (φ) and diagram 72 illustrates the tilt direction (θ).

Diagram 80 depicts the relative angle to the right direction versus thematching error.

Table 90 provides the average estimation error for tilt direction. Evenin the worst case scenario, the average prediction accuracy is less than20%.

FIG. 7 is a block/flow diagram of an exemplary method for performing apositional search process in an assembly task, in accordance with anembodiment of the present invention.

At block 102, for each training sample, normalize time-series data byapplying a variable transformation about right tilt direction (θ). Thetime series data can be obtained from a plurality of force sensorsmeasuring a force applied at different time periods to a, e.g., peg.

At block 104, build or create a time-series prediction model oftransformed training data.

At block 106, for a test sample, apply the variable transformation withdifferent directions.

At block 108, calculate matching ratio between the model created in thetraining phase and each of the transformed test data.

FIG. 8 is a block/flow diagram of an exemplary method for manipulatingtraining samples and test samples to accomplish the peg-in-hole task, inaccordance with an embodiment of the present invention.

Training samples 110 are input into the training phase module 120, whichcan communicate with a processor 122 and a memory 124. The trainingphase module 120 outputs a time-series model of transformed trainingdata 130, which are then provided to the test phase module 140. The testphase module 140 can communicate with a processor 142 and a memory 144.The test phase module 140 outputs data to a matching ratio calculator150, which in turn output estimation results 160 (of tilt direction) toa robotic system 170.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments described. Manymodifications and variations will be apparent to those of ordinaryskills in the art without departing from the scope and spirit of thedescribed embodiments. The terminology used herein was chosen to bestexplain the one or more embodiments, the practical application ortechnical improvement over technologies found in the marketplace, or toenable others of ordinary skills in the art to understand theembodiments described herein.

The present invention can be a system, a method, and/or a computerprogram product. The computer program product can include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium can be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network can includecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention can be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions can execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer can be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection can be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) can execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions can be provided to at leastone processor of a general purpose computer, special purpose computer,or other programmable data processing apparatus to produce a machine,such that the instructions, which execute via the processor of thecomputer or other programmable data processing apparatus, create meansfor implementing the functions/acts specified in the flowchart and/orblock diagram block or blocks or modules. These computer readableprogram instructions can also be stored in a computer readable storagemedium that can direct a computer, a programmable data processingapparatus, and/or other devices to function in a particular manner, suchthat the computer readable storage medium having instructions storedtherein includes an article of manufacture including instructions whichimplement aspects of the function/act specified in the flowchart and/orblock diagram block or blocks or modules.

The computer readable program instructions can also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational blocks/steps to be performed on thecomputer, other programmable apparatus or other device to produce acomputer implemented process, such that the instructions which executeon the computer, other programmable apparatus, or other device implementthe functions/acts specified in the flowchart and/or block diagram blockor blocks or modules.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which includes one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks can occur out of theorder noted in the figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

Reference in the specification to “one embodiment” or “an embodiment” ofthe present principles, as well as other variations thereof, means thata particular feature, structure, characteristic, and so forth describedin connection with the embodiment is included in at least one embodimentof the present principles. Thus, the appearances of the phrase “in oneembodiment” or “in an embodiment”, as well any other variations,appearing in various places throughout the specification are notnecessarily all referring to the same embodiment.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

Having described preferred embodiments of a system and method forperforming a peg-in-hole task with unknown tilt (which are intended tobe illustrative and not limiting), it is noted that modifications andvariations can be made by persons skilled in the art in light of theabove teachings. It is therefore to be understood that changes may bemade in the particular embodiments described which are within the scopeof the invention as outlined by the appended claims. Having thusdescribed aspects of the invention, with the details and particularityrequired by the patent laws, what is claimed and desired protected byLetters Patent is set forth in the appended claims.

1. A computer-implemented method executed by a robotic system forperforming a positional search process in an assembly task, the methodcomprising: applying forces to a first component to be inserted into asecond component; detecting the forces applied to the first component byemploying a plurality of force sensors attached to a robotic arm of therobotic system; extracting training samples corresponding to the forcesapplied to the first component; normalizing time-series data for each ofthe training samples by applying a variable transformation about a righttilt direction; creating a time-series prediction model of transformedtraining data; applying the variable transformation with differentdirections for a test sample; and calculating a matching ratio betweenthe created time-series prediction model and the transformed testsample.
 2. The method of claim 1, further comprising outputting adirection value having a best matching value as an estimation result. 3.The method of claim 1, wherein the time-series data includessix-dimensional time-series data.
 4. The method of claim 3, wherein onepair of the time-series data includes input forces.
 5. The method ofclaim 4, wherein another pair of the time-series data includes forcesensor values.
 6. The method of claim 1, wherein another pair of thetime-series data includes force sensor moments.
 7. The method of claim1, wherein calculating the matching ratio includes determining a sum ofsquares of each time point when a force is applied to the firstcomponent.
 8. A robotic system for performing a positional searchprocess in an assembly task, the robotic system comprising: a roboticarm; and a control system communicatively coupled to the robotic arm,the control system storing executable program instructions for causingthe robotic arm to perform the steps of: applying forces to a firstcomponent to be inserted into a second component; detecting the forcesapplied to the first component by employing a plurality of force sensorsattached to the robotic arm; extracting training samples correspondingto the forces applied to the first component; normalizing time-seriesdata for each of the training samples by applying a variabletransformation about a right tilt direction; creating a time-seriesprediction model of transformed training data; applying the variabletransformation with different directions for a test sample; andcalculating a matching ratio between the created time-series predictionmodel and the transformed test sample.
 9. The robotic system of claim 8,wherein a direction value having a best matching value is output as anestimation result.
 10. The robotic system of claim 8, wherein thetime-series data includes six-dimensional time-series data.
 11. Therobotic system of claim 10, wherein one pair of the time-series dataincludes input forces.
 12. The robotic system of claim 11, whereinanother pair of the time-series data includes force sensor values. 13.The robotic system of claim 12, wherein another pair of the time-seriesdata includes force sensor moments.
 14. The robotic system of claim 8,wherein calculating the matching ratio includes determining a sum ofsquares of each time point when a force is applied to the firstcomponent.
 15. A robotic system, comprising: a robot constructed toassemble a first component to a second component; at least one sensorcoupled to the robot; a control system communicatively coupled to therobot and to the at least one sensor, the control system storingexecutable program instructions for executing assembly motion of therobot; and a learning device communicatively coupled to the controlsystem and operative to direct the robot via the control system, thecontrol system performing the steps of: extracting training samplescorresponding to the forces applied to the first component; normalizingtime-series data for each of the training samples by applying a variabletransformation about a right tilt direction; creating a time-seriesprediction model of transformed training data; applying the variabletransformation with different directions for a test sample; andcalculating a matching ratio between the created time-series predictionmodel and the transformed test sample.
 16. The robotic system of claim15, wherein the time-series data includes six-dimensional time-seriesdata.
 17. The robotic system of claim 16, wherein one pair of thetime-series data includes input forces.
 18. The robotic system of claim17, wherein another pair of the time-series data includes force sensorvalues.
 19. The robotic system of claim 18, wherein another pair of thetime-series data includes force sensor moments.
 20. The robotic systemof claim 15, wherein calculating the matching ratio includes determininga sum of squares of each time point when a force is applied to the firstcomponent.